Preheat your oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper and arrange 16 Oreo cookies in a single layer on the bottom, in 4 rows of 4.
Melt the butter and chopped chocolate together in a large microwave-safe bowl in 30 second bursts, stirring each time, until smooth. Whisk in both sugars and let the mixture cool for 5 minutes.
Whisk in the yogurt and vanilla until the batter looks smooth and glossy.
In a separate bowl, whisk the flour, cocoa powder, baking soda and salt. Fold into the chocolate mixture just until no dry streaks remain.
Pour the batter over the Oreos and gently spread it to cover them completely. Roughly chop the remaining 6 Oreos, scatter them over the top and press lightly into the batter.
Bake for 28 to 32 minutes, until the edges are set and a toothpick inserted in the center comes out with moist crumbs.
Let the brownies cool completely in the pan, about 2 hours. Lift them out and cut into 16 squares, following the rows so each brownie has a whole Oreo hidden inside.